相关论文: Quaternionic Electroweak Theory and CKM Matrix
We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar…
We perform a one-dimensional complexified quaternionic version of the Dirac equation based on $i$-complex geometry. The problem of the missing complex parameters in Quaternionic Quantum Mechanics with $i$-complex geometry is overcome by a…
We complete the rules of translation between standard complex quantum mechanics (CQM) and quaternionic quantum mechanics (QQM) with a complex geometry. In particular we describe how to reduce ($2n$+$1$)-dimensional complex matrices to {\em…
The aim of the paper is to propose one paradigm change of CKM global fits on experimental data from electroweak sector. The change refers to using in fits the exact unitarity constraints expressed in terms of four invariant parameters, such…
This study examines Quaternion Dirac solutions for an infinite square well. The quaternion result does not recover the complex result within a particular limit. This raises the possibility that quaternionic quantum mechanics may not be…
The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.
A new method for computing hadronic effects on electroweak radiative corrections to low-energy weak interaction semileptonic processes is described. It employs high order perturbative QCD results originally derived for the Bjorken sum rule…
A viable formulation of gauge theory with extra generations in terms of quaternionic fields is presented. For the theory to be acceptable, the number of generations should be equal to or greater than 4. The quark-lepton mass matrices are…
A simple translation between a standard representation of $\mathfrak{sl}_2\mathbb{C}$ and the complex-quaternions ($\mathbb{H}\otimes_\mathbb{R}\mathbb{C}$) is established and exploited to construct a novel hyper-complex description of the…
In this work we show the quaternionic quantum descriptions of physical processes from the Planck to macro scale. The results presented here are based on the concepts of the Cauchy continuum and the elementary cell at the Planck scale. The…
Schemes for fermion masses should predict elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. We review the freedom allowed by present experiments and how the parameter space will shrink in the next few years. In addition to experiments…
A physical model which describes the CKM matrix is analyzed. The elements of such a matrix are field-strength renormalization factors. Each column gives the probability amplitude for the field operators of the coupled Lagrangian to create a…
Solutions of quaternionic quantum mechanics (QQM) are difficult to grasp, even in simple physical situations. In this article, we provide simple and understandable free particle quaternionic solutions, that can be easily compared to complex…
The angle $\gamma$ of the standard CKM unitarity triangle can be determined from tree-level $B$-meson decays essentially without hadronic uncertainties. We calculate the second-order electroweak corrections for the $B \to D \pi$ modes and…
The status of lattice calculations of heavy quark phenomenology is reviewed. Particular emphasis is placed on the understanding and control of the calculational uncertainties. The ensuing implications for constraining the CKM matrix…
A simple inspection of the one loop quark self-energy suggests a prescription of the CKM matrix renormalization in the standard model. It leads to a CKM matrix counterterm which is gauge parameter independent and satisfies the unitarity…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
We consider non-local properties of quanternionic quantum mechanics, in which the complex numbers are replaced by the quaternions as the underlying algebra. Specifically, we show that it is possible to construct a non-local box. This allows…
The experimental status and theoretical uncertainties of the Cabibbo--Kobayashi--Maskawa (CKM) matrix describing the charge-changing weak transitions between quarks with charges -1/3 ($d, s, b$) and 2/3 ($u, c, t$) are reviewed. Some recent…
We introduce four fundamental quantum numbers based on the $D_4$ root system, giving a unified description of quarks and leptons. These numbers will make it possible to define electric charge in a simple way. By postulating a fundamental…